New Dynamic Response Surface Methodology for Modeling Nonlinear Processes over Semi-infinite Time Horizons

Abstract

We follow up on the recently proposed Dynamic Response Surface Methodology (DRSM) [Klebanov and Georgakis Ind. Eng. Chem. Res. 2016, 55(14), 4022] as an effective data-driven approach for modeling time-varying outputs of batch processes with finite time durations. The present new DRSM methodology, DRSM-2, is capable of accurately modeling nonlinear continuous processes over both finite and semi-infinite time horizons as easily and accurately as modeling batch processes, as DRSM-1 did in the initial publication, cited above. The key innovation here is the introduction of an exponential transformation of time, converting the semi-infinite time duration into a finite one. We also propose a systematic model selection procedure to determine the optimal values of the decision parameters affecting the accuracy of the obtained DRSM-2 model. We demonstrate the power of the DRSM-2 approach in two representative processes, a continuous propylene polymerization and a semibatch penicillin fermentation. It is shown that the obtained data-driven models accurately represent the time-varying process outputs in both of the examined, and quite different, case studies.

Combining model structure identification and hybrid modelling for photo‐production process predictive simulation and optimisation

“…In this study, a 2nd degree polynomial regression (PR) model shown as Equation (2b) was selected as the data‐driven model to estimate the mismatch between the kinetic model and the process data second‐degree PRs have been predominantly used in response surface methodology for optimal experimental design and analysis (Aguirre & Bassi, 2013; J. Wang & Wan, 2008). Their use has been extended into dynamic systems through the recent progress in dynamic response surface methodology (Z. Wang & Georgakis, 2017). Moreover, a 2nd degree PR is also known as an extension of the Lotka‐Volterra model (Guerra, 2014), a classic model used to understand the interactions of communities in microbiome studies.…”

Automatic data‐driven stoichiometry identification and kinetic modeling framework for homogeneous organic reactions

“…To handle the time‐resolved output data from DoE, which is a typical requirement for reaction dynamic modeling, Klebanov and Georgakis 26 proposed DRSM, a data‐driven model that can effectively capture the relationship between process input conditions and time‐resolved outputs. Compared to the original DRSM method, Wang and Georgakis 27 proposed to use the exponential transformation of time as variable for modeling nonlinear processes over semi‐infinite horizons. Dong, Georgakis, et al 15 applied this method for pharmaceutical reaction modeling, and made improvements to obtain more accurate models by fixing the initial concentration of reactants together with forcing the concentration output to be non‐negative.…”

Stoichiometry identification of pharmaceutical reactions using the constrained dynamic response surface methodology

“…The original DRSM algorithm (DRSM-1) has been improved by using an exponential time transformation 5 to allow semi-infinite time intervals. It was further modified for the modeling of concentration profiles by imposing regression constraints, motivated by our qualitative understanding of such profiles.…”

“…The dynamic response surface methodology (DRSM) provides an input–output model based on time‐resolved measurements in a set of experiments from the design of experiments (DoE) or, the recently developed, design of dynamic experiments (DoDE) methodologies. The original DRSM algorithm (DRSM‐1) has been improved by using an exponential time transformation to allow semi‐infinite time intervals. It was further modified for the modeling of concentration profiles by imposing regression constraints, motivated by our qualitative understanding of such profiles.…”